Driving natural systems: Chemical energy production and usensjones/lec-mito.pdf · Driving natural...

Driving naturalsystems: Chemicalenergy production

and use

Chemical energyand metabolism

ATP usage andproduction

Mitochondria andbioenergeticcontrol

Modelling systemsof chemicalreactions

Driving natural systems: Chemicalenergy production and use


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Metabolism

I Metabolism: the sum of thephysical and chemical processesin an organism by which itsmaterial substance is produced,maintained, and destroyed[anabolism], and by whichenergy is made available[catabolism]

I Metabolism allows organisms tocontrol biomass and energy

I A set of chemicaltransformations, oftenenzyme-catalysed

I A complicated network:simplified through tools like fluxbalance analysis

I Metabolism provides the energyfor inference and control

I Metabolism is itself controlledand regulated: metabolic controlanalysis, active regulation


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Free energy

I Energy that can be harnessed to perform workI At constant temperature and pressure (which we shall assume), the

appropriate expression is the Gibbs free energy G(p,T )

G(p,T ) = U + pV − TS

I Internal energy U, pressure p, volume V , temperature T , entropy SI Change in free energy, where αj ,Xj are a feature and associated

potential that influence our system (e.g. N, µ: copy number andchemical potential of chemical species):

dG = Vdp − SdT +∑

i

µi dNi −∑

j

Xj dαj

I We’ll consider chemical reactions, which take place at fixed p and TI Particle numbers Ni may be changed by reactions, and we also have to

include the pair {∆Ψ, q} for charge across a membrane potentialI Our Gibbs free energy change

dG =∑

i

µi dNi − F∆Ψdq


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Energy from chemical reactionsI Reversible chemical reaction with Si substrates, Pi products, and

stoichiometry given by ai , bi :

a1S1 + a2S2 + ... b1P1 + b2P2 + ...

I Change in free energy

dG =∑

i

µi dNi − F∆Ψdq

I Chemical potential µ is a measure of the ‘concentration gradient’ in asystem

µi ∼ µ0i + RT ln ci

I For above reaction:

µSidNSi

= (µ0Si

+ RT ln[Si ])× (−ai )

µPidNPi

= (µ0Pi

+ RT ln[Pi ])× bi∑i

µi dNi = C(a,b, µ0) + RT∑

j

ln[Pj ]bj − RT

∑j

ln[Sj ]aj

I Broadly, if Z is total charge carried through a potential ∆Ψ(∆Ψmito ' −160 mV):

∆G = ∆G0 + RT ln

(∏i [Pi ]

bi∏i [Si ]ai

)− ZF∆Ψ


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Activation energies

I ∆G = ∆G0 + RT ln(∏

i [Pi ]bi∏

i [Si ]ai

)− ZF∆Ψ

I Reactions with a negative ∆G net release energy and are sometimesdescribed as ‘happening spontaneously’

I There is still an activation energy / geometric contraints to overcome(though this is sometimes possible to do thermally)

I ∆G doesn’t tell us how fast a reaction will progress


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Rates of chemical reactionsI Chemical reaction

a1S1 + a2S2 + ... b1P1 + b2P2 + ...

I Law of mass action: reaction rate ν ∝ collision probability ∝ reactantconcentration [Xi ]

ν = ν+ − ν− = k+

∏i

[Si ]ai − k−

∏j

[Pj ]bj

I Equilibrium constant is calculated when ν+ = ν−

keq =k+

k−=

∏[Peq

j ]bj∏[Seq

i ]ai

I At equilibrium, in absence of charge coupling:

0 = ∆G = ∆G0 + RT ln

(∏i [Pi ]

bi∏i [Si ]ai

)

I So∆G0 = −RT ln keq

I Negative ∆G0 → k+ > k− → forward reaction


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ATP (adenosine triphosphate) as a cellular fuel source

I ATP is used to provide energy for most energy-demanding cellularprocesses

I Neurotransmitter synthesis: provides the energy for inferenceI Gene expression and regulation: provides the energy for controlI Muscle contraction: motionI Active transport across membranesI How do organisms synthesise and obtain energy from ATP?

http://highered.mcgraw-hill.com/sites/0072495855/student_view0/chapter10/animation__breakdown_of_atp_and_cross-bridge_movement_during_muscle_contraction.html

http://www.wiley.com/college/boyer/0470003790/animations/membrane_transport/membrane_transport.htm


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ATP (adenosine triphosphate) as a cellular fuel source

I Two phosphate bonds which may be hydrolysed, releasing energy (ATP↔ ADP↔ AMP)

I Cells maintain ATP/ADP ratio out of equilibriumI ATP + H2O → ADP + Pi ; ∆G0 = −30.5 kJ mol−1

I Under physiological conditions and typical cellular ATP/ADP ratio,∆G ' −(40− 60) kJ mol−1

I ‘Energy charge’ sometimes used for energetic status

[ATP] + 12 [ADP]

[ATP] + [ADP] + [AMP]

I The human body contains 0.2 mol ATP. We require the hydrolysis of100-150 mol ATP per day (50-75 kg). Each ATP molecule is recycled500-750 times per day.


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ATP production

I ATP + H2O → ADP + Pi ; ∆G0 = −30.5 kJ mol−1

I Under physiological conditions and typical cellular ATP/ADP ratio,∆G ' −(40− 60) kJ mol−1

I But this is net energy release – ATP rarely breaks down on its own (itwould be a poor energy currency if it did)

I Proteins that harness ATP are usually ATPases – i.e. enzymes thatcatalyse the hydrolysis of ATP (hence overcoming the activation energy)


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Some other players in bioenergetics

I NADH: an electron donor used to transfer high-energy e−(NADH + H+ + 1

2 O2 NAD+ + H2O : ∆G0 = −220 kJ mol−1 – oneNADH used to synthesis several ATP)

I Means of producing ATP (and NADH):I Glycolysis: energy production without oxygen (glucose→ 2

pyruvate + 2 ATP + NADH + H+)I Krebs cycle / citric acid cycle / TCA cycle: a circular set of

reactions that takes in ‘fuel’ once per cycle and feeds oxidativerespiration (we’ll look at this in the practical)

I Oxidative phosphorylation: energetic e− power proton pumps,setting up a harnessable electrochemical gradient

I Fermentation (glucose→ lactic acid)I Photosynthesis (photons, proton pumps)I Replenishment with nucleoside diphosphate kinases (GTP→

GDP)


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Oxidative phosphorylation


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I (Biochemical detail is not examinable)I Krebs cycle produces NADH and succinateI A series of complexes pump protons through the inner mitochondrial

membraneI Complex I: NADH + H+ → NAD+, pumps 4 protons, reduces coenzyme

QI Complex II: succinate→ fumarate, reduces coenzyme QI Complex III: Oxidises coenzyme Q, reduces cytochrome C, pumps 4

protonsI Complex IV: Reduces cytochrome C, pumps 2 protonsI Electrochemical potential (charge separation + chemical gradient) set up

across membrane


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I Complex V: energetic protons flow backinto matrix

I F1 subunit in membrane; Fo subunit inthe matrix

I (Amazing structure best understood byviewing animation)

I Structure and function: John E. Walker,1997 Nobel Prize in Chemistry

http://www.sumanasinc.com/webcontent/animations/content/atpsynthase.html


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Energy and life

I Nick Lane: energy per gene expressed is key factor in evolution ofcomplex life

I Local mitochondrial genomes: local control of mitochondriaI Alternative 1: non-local genome, power sources not individually

addressableI Alternative 2: many full genomes localised to power generation: huge

amount of nucleic acidI Mitochondria: small, individually addressable genomes localised to

power generation

I ‘... being large and havingmasses of DNA is not enough toattain complexity: cells need tocontrol energy coupling across awide area of membranes usingsmall, high copy, bioenergeticallyspecialized genomes likemtDNA’

I Express 2× 105 more geneswith no energy penalty


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Mitochondrial bioenergetic control

I How can mitochondria be individually addressed by control?I ‘Quality control’: individual mitochondrial performance is sensed

(membrane potential ∆Ψ and others)?I Good mitochondria are allowed to fuse into a network and remain safe

from degradationI Bad mitochondria remain fragmented and, if they don’t recover, are

targeted for authophagy and recyclingI An exercise: how does this map to the types of control we have

considered?


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Control on mitochondrial respiration

I Cells with ‘good’ and ‘bad’ mitochondria show little difference inrespiration rate

I There are pronounced physiological differences but compensatorymechanisms exist to control respiration (this is modern and debatedresearch)

I Bad mitochondria produce more ROS (damaging ‘exhaust’) productionthan good mitochondria

I Cells producing more ROS have more mtDNAI → Cells with bad mitochondria produce more mitochondria to retain

overall respiratory capacityI An exercise: how does this map to the types of control we have

considered?


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Modelling systems of chemical reactions

I We will look at several ways of modelling the chemical processes thatdrive natural systems

I Now: ODE modelling – physical models for the species concentrationsand physical properties of bioenergetic systems (particularly oxidativephosphorylation and the mitochondrion)

I Next: FBA (flux balance analysis) – coarse-grained representation oflarge networks of metabolic components with constraints andoptimisations

I Then: MCA (metabolic control analysis) – analysis of how fluxes andconcentrations in metabolic networks respond to perturbations innetwork properties


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A simple example of ODE modelling

I Adenylate kinases swap high-energy phosphates between adenosineframes in the inter-membrance space of the mitochondrion

2ADP ATP + AMP

I Rate of this reaction

ν = ν+ − ν− = k+

∏[Si ]

mi − k−∏

[Pj ]mj

= k+[ADP]2 − k−[AMP][ATP]

≡ XAK

(KAK [ADP]2 − [AMP][ATP]

)I XAK is the activity; KAK the reaction parameter

I For example, d [ATP]dt = ν/V


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An electrochemical example

I Complex I uses energy from NADH electrons to pump protons out of themitochondrial matrix

H+ + NADH + Q NAD+ + QH2 + 4∆H+

I 4∆H+ represents four protons pumped across the membraneI These protons need to work against an electrochemical gradient:

∆GH = RT ln(

[H+]out[H+]in

)− F∆Ψ

I Reaction rate ∝ collision probabilityI We also have dependence on ‘proton flux probability’ represented by the

Boltzmann factor e−∆GH/RT /ZI (Model) combination:

reaction rate ν ∝ (collision probability) × (proton flux probability)

∝ (concentrations) × (Boltzmann factor)

ν = k ′+[H+][NADH][Q]− k ′−[NAD+][QH2]e4∆GH/RT

≡ X ′CI

(K ′CI [H

+][NADH][Q]− [NAD+][QH2]e4∆GH/RT)


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Systems of chemical ODEs


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Systems of chemical ODEs elucidate biochemical control

I Simulation of physiological ODE model allows us to determine thatphosphate control acts on Complex III flux:

I Can’t match data without ∝ (1 + [Pi ]/k1)/(1 + [Pi ]/k2) termI We will explore other features of this model in the practical.

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